Question

Two cylinders fitted with pistons contain equal amount of an ideal diatomic gas at 300 K. The piston of A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of gas in B is

• A. 30 K
• B. 18 K
• C. 50 K
• D. 42 K

Answer 1

The correct option is D 42 K

Process in cylinder A is constant pressure process.
Process in cylinder B is constant volume process.
Heat supplied is :
$Q=n{C}_p\Delta T_1$
$Q=n{C}_v\Delta T_2$
$\frac{C_p}{C_v}=\frac{\Delta T_2}{\Delta T_1}=\gamma$
For a monoatomic gas is
$\gamma =\frac{7}{5}$
Hence $T_2=\frac{7}{5}\times 30=42K$
Option D is correct.